<< Chapter < Page Chapter >> Page >

Phase detector

The goal of the PLL is to maintain a demodulating sine and cosine that match the incoming carrier. Suppose ω c is the believed digital carrier frequency. We can then represent the actual received carrier frequency as theexpected carrier frequency with some offset, ω c ˜ ω c θ ˜ n . The NCO generates the demodulating sine and cosine with the expected digital frequency ω c and offsets this frequency with the output of the loop filter. The NCO frequency can then be modeled as ω c ^ ω c θ ^ n . Using the appropriate trigonometric identities A B 1 2 A B A B and A B 1 2 B A A B . , the in-phase and quadrature signals can be expressed as

z 0 n 1 2 θ ˜ n θ ^ n 2 ω c θ ˜ n θ ^ n
z Q n 1 2 θ ˜ n θ ^ n 2 ω c θ ˜ n θ ^ n
After applying a low-pass filter to remove the double frequency terms, we have
y 1 n 1 2 θ ˜ n θ ^ n
y Q n 1 2 θ ˜ n θ ^ n
Note that the quadrature signal, z Q n , is zero when the received carrier and internallygenerated waves are exactly matched in frequency and phase. When the phases are only slightly mismatched we can use therelation
θ small θ θ
and let the current value of the quadrature channel approximate the phase difference: z Q n θ ˜ n θ ^ n . With the exception of the sign error, this difference is essentially how much we need to offset our NCOfrequency If θ ˜ n θ ^ n 0 then θ ^ n is too large and we want to decrease our NCO phase. . To make sure that the sign of the phase estimate is right, in this example the phase detector issimply negative one times the value of the quadrature signal. In a more advanced receiver, information from boththe in-phase and quadrature branches is used to generate an estimate of the phase error. What should the relationship between the I and Q branches be fora digital QPSK signal?

Loop filter

The estimated phase mismatch estimate is fed to the NCO via a loop filter, often a simple low-pass filter. For thisexercise you can use a one-tap IIR filter,

y n β x n α y n 1
To ensure unity gain at DC, we select β 1 α

It is suggested that you start by choosing α 0.6 and K 0.15 for the loop gain. Once you have a working system, investigate the effects of modifying these values.

Matlab simulation

Simulate the PLL system shown in [link] using MATLAB. As with the DLL simulation, you will have to simulate the PLL on a sample-by-sample basis.

Use [link] to implement your NCO in MATLAB. However, to ensure that the phase term does not grow toinfinity, you should use addition modulo 2 in the phase update relation. This can be done by setting θ n θ n 2 whenever θ n 2 .

[link] illustrates how the proposed PLL will behave when given a modulated BPSK waveform. In this case thetransmitted carrier frequency was set to ω c ˜ 2 1024 to simulate a frequency offset.

Output of PLL sub-system for BPSK modulated carrier.

Note that an amplitude transition in the BPSK waveform is equivalent to a phase shift of the carrier by 2 . Immediately after this phase change occurs, the PLL begins to adjust the phase to force the quadraturecomponent to zero (and the in-phase component to 1 2 ). Why would this phase detector not work in a real BPSK environment? How could it be changed to work?

Questions & Answers

how to know photocatalytic properties of tio2 nanoparticles...what to do now
Akash Reply
it is a goid question and i want to know the answer as well
Do somebody tell me a best nano engineering book for beginners?
s. Reply
what is fullerene does it is used to make bukky balls
Devang Reply
are you nano engineer ?
what is the Synthesis, properties,and applications of carbon nano chemistry
Abhijith Reply
Mostly, they use nano carbon for electronics and for materials to be strengthened.
is Bucky paper clear?
so some one know about replacing silicon atom with phosphorous in semiconductors device?
s. Reply
Yeah, it is a pain to say the least. You basically have to heat the substarte up to around 1000 degrees celcius then pass phosphene gas over top of it, which is explosive and toxic by the way, under very low pressure.
Do you know which machine is used to that process?
how to fabricate graphene ink ?
for screen printed electrodes ?
What is lattice structure?
s. Reply
of graphene you mean?
or in general
in general
Graphene has a hexagonal structure
On having this app for quite a bit time, Haven't realised there's a chat room in it.
what is biological synthesis of nanoparticles
Sanket Reply
what's the easiest and fastest way to the synthesize AgNP?
Damian Reply
types of nano material
abeetha Reply
I start with an easy one. carbon nanotubes woven into a long filament like a string
many many of nanotubes
what is the k.e before it land
what is the function of carbon nanotubes?
I'm interested in nanotube
what is nanomaterials​ and their applications of sensors.
Ramkumar Reply
what is nano technology
Sravani Reply
what is system testing?
preparation of nanomaterial
Victor Reply
Yes, Nanotechnology has a very fast field of applications and their is always something new to do with it...
Himanshu Reply
good afternoon madam
what is system testing
what is the application of nanotechnology?
In this morden time nanotechnology used in many field . 1-Electronics-manufacturad IC ,RAM,MRAM,solar panel etc 2-Helth and Medical-Nanomedicine,Drug Dilivery for cancer treatment etc 3- Atomobile -MEMS, Coating on car etc. and may other field for details you can check at Google
anybody can imagine what will be happen after 100 years from now in nano tech world
after 100 year this will be not nanotechnology maybe this technology name will be change . maybe aftet 100 year . we work on electron lable practically about its properties and behaviour by the different instruments
name doesn't matter , whatever it will be change... I'm taking about effect on circumstances of the microscopic world
how hard could it be to apply nanotechnology against viral infections such HIV or Ebola?
silver nanoparticles could handle the job?
not now but maybe in future only AgNP maybe any other nanomaterials
I'm interested in Nanotube
this technology will not going on for the long time , so I'm thinking about femtotechnology 10^-15
can nanotechnology change the direction of the face of the world
Prasenjit Reply
how did you get the value of 2000N.What calculations are needed to arrive at it
Smarajit Reply
Privacy Information Security Software Version 1.1a
Berger describes sociologists as concerned with
Mueller Reply
Got questions? Join the online conversation and get instant answers!
QuizOver.com Reply

Get the best Algebra and trigonometry course in your pocket!

Source:  OpenStax, Digital signal processing laboratory (ece 420). OpenStax CNX. Sep 27, 2006 Download for free at http://cnx.org/content/col10236/1.14
Google Play and the Google Play logo are trademarks of Google Inc.

Notification Switch

Would you like to follow the 'Digital signal processing laboratory (ece 420)' conversation and receive update notifications?